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Vector subtraction

  1. Jun 11, 2012 #1
    1. The problem statement, all variables and given/known data

    For the vectors [itex]A^{→}[/itex] and [itex]B^{→}[/itex], calculate the vector difference [itex]A^{→}[/itex] - [itex]B^{→}[/itex]. Magnitude of vector [itex]A^{→}[/itex] is 12 meters, with an angle of 180°. Magnitude of vector [itex]B^{→}[/itex] is 18 meters, with an angle of 37°.

    2. Relevant equations

    [itex]A{y}[/itex] = Asinθ; [itex]B{y}[/itex] = Bsinθ
    [itex]A{x}[/itex] = Acosθ; [itex]B{x}[/itex] =Bcosθ
    Resultant vector = [itex]\sqrt{Rx^{2} + Ry^{2}}[/itex]

    3. The attempt at a solution

    I know not providing a graph might make this problem a bit more difficult. I just really desperately need help on how to calculate vector subtraction because I'm not sure if I'm doing it right.

    I found that the x-component of vector [itex]A^{→}[/itex] is -12 meters and the y-component is 0 meter. The x-component of vector [itex]B^{→}[/itex] is 14.4 meters and the y-component is 10.8 meters. From that, the [itex]R{x}[/itex] would be 2.4 meters and [itex]R{y}[/itex] would be 10.8 meters.

    If I were to just do vector [itex]A^{→}[/itex] + [itex]B^{→}[/itex], I know how to calculate that. I would use the Resultant vector formula [itex]\sqrt{Rx^{2} + Ry^{2}}[/itex], which would give me of R = 11.06. But if I'm doing what this problem is doing, I don't know if that's the right formula to use.

    I understand that [itex]A^{→}[/itex] - [itex]B^{→}[/itex] is the same thing as -[itex]B^{→}[/itex] + [itex]A^{→}[/itex]. I was wondering how the negative part translated into the calculation. For example, do I make vector [itex]B^{→}[/itex]'s x-component negative (to -14.4 meters), and have the [itex]R{x}[/itex] = -26.4 meters and the [itex]R{y}[/itex] = -10.8 meters (because vector [itex]B^{→}[/itex]'s y-component would then be -10.8 mters)? And if all that is correct, would I carry on with the same resultant vector formula [itex]\sqrt{Rx^{2} + Ry^{2}}[/itex], plugging in the numbers to get R = 28.5 meters?

    Thank you so much for helping me!
     
  2. jcsd
  3. Jun 11, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The problem asks the vector difference, not only the magnitude of the difference vector. The components of the resultant difference vector are Ax-Bx and Ay-By.

    ehild
     
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